Solve a quantile regression(LAD is a special case) with a linear programing solver.

I use the optmodel. The results are the same as that from quantreg. In case one does not have it( optmode procedure), one can solve it with LP.

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%let n=300;
%let quantile=0.6;

data t1;
   do i=1 to &n;
      x=rannor(123);
      e=rannor(123);
      y=-1+1*x+e;
      output;
    end;
    keep y x;
run;

proc quantreg data=t1;
model y=x/quantile=&quantile;
run;

proc optmodel;
   set I = 1 .. &n;
   number y{I};
   number x{I};
   read data t1 into [_n_] y x ;
   var b0 init 0, b1 init 0;
   var u{k in I} >=0, v{k in I} >=0;

   min f = sum{k in I} (&quantile*u[k] + (1-&quantile)*v[k]);
  
   con target  {k in I}:  b0 + b1*x[k] + u[k] - v[k]=y[k];
        
reset printlevel=2;
   solve ;
   print f b0 b1;
quit;